thenall1710Consider fig: SR²(1) Give(11) Giveongiven by f(x)=xexplicit homotoptopyexplicit homotopy from g to ffrom f to gong(x) = (90)

Answered: Consider fig: SR² (1) bive (11) Give on…

Consider fig: SR² (1) bive (11) Give on given by f(x)=x explicit homotopy from it to g explicit homotopy from g to f f g+) = (0,0)

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

then
all
1
7
10
Consider fig: SR²
(1) Give
(11) Give
on
given by f(x)=x
explicit homotop
topy
explicit homotopy from g to f
from f to g
on
g(x) = (90)

Expert Solution

Step 1

Given that, f,g are functions from S¹ to R given by f(X) = X and g(X) = (0,0)

Now, let us consider the function F from S¹×[0,1] to R defined by

F(s,0) = s = f(s), F(s,1) =(0,0) = g(s) and otherwise F(s,t) = (s,t)

Therefore, F is a homotopy from f to g.

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